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        "%matplotlib inline"
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      "source": [
        "\n# Comparing different clustering algorithms on toy datasets\n\n\nThis example shows characteristics of different\nclustering algorithms on datasets that are \"interesting\"\nbut still in 2D. With the exception of the last dataset,\nthe parameters of each of these dataset-algorithm pairs\nhas been tuned to produce good clustering results. Some\nalgorithms are more sensitive to parameter values than\nothers.\n\nThe last dataset is an example of a 'null' situation for\nclustering: the data is homogeneous, and there is no good\nclustering. For this example, the null dataset uses the\nsame parameters as the dataset in the row above it, which\nrepresents a mismatch in the parameter values and the\ndata structure.\n\nWhile these examples give some intuition about the\nalgorithms, this intuition might not apply to very high\ndimensional data.\n\n"
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        "print(__doc__)\n\nimport time\nimport warnings\n\nimport numpy as np\nimport matplotlib.pyplot as plt\n\nfrom sklearn import cluster, datasets, mixture\nfrom sklearn.neighbors import kneighbors_graph\nfrom sklearn.preprocessing import StandardScaler\nfrom itertools import cycle, islice\n\nnp.random.seed(0)\n\n# ============\n# Generate datasets. We choose the size big enough to see the scalability\n# of the algorithms, but not too big to avoid too long running times\n# ============\nn_samples = 1500\nnoisy_circles = datasets.make_circles(n_samples=n_samples, factor=.5,\n                                      noise=.05)\nnoisy_moons = datasets.make_moons(n_samples=n_samples, noise=.05)\nblobs = datasets.make_blobs(n_samples=n_samples, random_state=8)\nno_structure = np.random.rand(n_samples, 2), None\n\n# Anisotropicly distributed data\nrandom_state = 170\nX, y = datasets.make_blobs(n_samples=n_samples, random_state=random_state)\ntransformation = [[0.6, -0.6], [-0.4, 0.8]]\nX_aniso = np.dot(X, transformation)\naniso = (X_aniso, y)\n\n# blobs with varied variances\nvaried = datasets.make_blobs(n_samples=n_samples,\n                             cluster_std=[1.0, 2.5, 0.5],\n                             random_state=random_state)\n\n# ============\n# Set up cluster parameters\n# ============\nplt.figure(figsize=(9 * 2 + 3, 12.5))\nplt.subplots_adjust(left=.02, right=.98, bottom=.001, top=.96, wspace=.05,\n                    hspace=.01)\n\nplot_num = 1\n\ndefault_base = {'quantile': .3,\n                'eps': .3,\n                'damping': .9,\n                'preference': -200,\n                'n_neighbors': 10,\n                'n_clusters': 3,\n                'min_samples': 20,\n                'xi': 0.05,\n                'min_cluster_size': 0.1}\n\ndatasets = [\n    (noisy_circles, {'damping': .77, 'preference': -240,\n                     'quantile': .2, 'n_clusters': 2,\n                     'min_samples': 20, 'xi': 0.25}),\n    (noisy_moons, {'damping': .75, 'preference': -220, 'n_clusters': 2}),\n    (varied, {'eps': .18, 'n_neighbors': 2,\n              'min_samples': 5, 'xi': 0.035, 'min_cluster_size': .2}),\n    (aniso, {'eps': .15, 'n_neighbors': 2,\n             'min_samples': 20, 'xi': 0.1, 'min_cluster_size': .2}),\n    (blobs, {}),\n    (no_structure, {})]\n\nfor i_dataset, (dataset, algo_params) in enumerate(datasets):\n    # update parameters with dataset-specific values\n    params = default_base.copy()\n    params.update(algo_params)\n\n    X, y = dataset\n\n    # normalize dataset for easier parameter selection\n    X = StandardScaler().fit_transform(X)\n\n    # estimate bandwidth for mean shift\n    bandwidth = cluster.estimate_bandwidth(X, quantile=params['quantile'])\n\n    # connectivity matrix for structured Ward\n    connectivity = kneighbors_graph(\n        X, n_neighbors=params['n_neighbors'], include_self=False)\n    # make connectivity symmetric\n    connectivity = 0.5 * (connectivity + connectivity.T)\n\n    # ============\n    # Create cluster objects\n    # ============\n    ms = cluster.MeanShift(bandwidth=bandwidth, bin_seeding=True)\n    two_means = cluster.MiniBatchKMeans(n_clusters=params['n_clusters'])\n    ward = cluster.AgglomerativeClustering(\n        n_clusters=params['n_clusters'], linkage='ward',\n        connectivity=connectivity)\n    spectral = cluster.SpectralClustering(\n        n_clusters=params['n_clusters'], eigen_solver='arpack',\n        affinity=\"nearest_neighbors\")\n    dbscan = cluster.DBSCAN(eps=params['eps'])\n    optics = cluster.OPTICS(min_samples=params['min_samples'],\n                            xi=params['xi'],\n                            min_cluster_size=params['min_cluster_size'])\n    affinity_propagation = cluster.AffinityPropagation(\n        damping=params['damping'], preference=params['preference'])\n    average_linkage = cluster.AgglomerativeClustering(\n        linkage=\"average\", affinity=\"cityblock\",\n        n_clusters=params['n_clusters'], connectivity=connectivity)\n    birch = cluster.Birch(n_clusters=params['n_clusters'])\n    gmm = mixture.GaussianMixture(\n        n_components=params['n_clusters'], covariance_type='full')\n\n    clustering_algorithms = (\n        ('MiniBatchKMeans', two_means),\n        ('AffinityPropagation', affinity_propagation),\n        ('MeanShift', ms),\n        ('SpectralClustering', spectral),\n        ('Ward', ward),\n        ('AgglomerativeClustering', average_linkage),\n        ('DBSCAN', dbscan),\n        ('OPTICS', optics),\n        ('Birch', birch),\n        ('GaussianMixture', gmm)\n    )\n\n    for name, algorithm in clustering_algorithms:\n        t0 = time.time()\n\n        # catch warnings related to kneighbors_graph\n        with warnings.catch_warnings():\n            warnings.filterwarnings(\n                \"ignore\",\n                message=\"the number of connected components of the \" +\n                \"connectivity matrix is [0-9]{1,2}\" +\n                \" > 1. Completing it to avoid stopping the tree early.\",\n                category=UserWarning)\n            warnings.filterwarnings(\n                \"ignore\",\n                message=\"Graph is not fully connected, spectral embedding\" +\n                \" may not work as expected.\",\n                category=UserWarning)\n            algorithm.fit(X)\n\n        t1 = time.time()\n        if hasattr(algorithm, 'labels_'):\n            y_pred = algorithm.labels_.astype(np.int)\n        else:\n            y_pred = algorithm.predict(X)\n\n        plt.subplot(len(datasets), len(clustering_algorithms), plot_num)\n        if i_dataset == 0:\n            plt.title(name, size=18)\n\n        colors = np.array(list(islice(cycle(['#377eb8', '#ff7f00', '#4daf4a',\n                                             '#f781bf', '#a65628', '#984ea3',\n                                             '#999999', '#e41a1c', '#dede00']),\n                                      int(max(y_pred) + 1))))\n        # add black color for outliers (if any)\n        colors = np.append(colors, [\"#000000\"])\n        plt.scatter(X[:, 0], X[:, 1], s=10, color=colors[y_pred])\n\n        plt.xlim(-2.5, 2.5)\n        plt.ylim(-2.5, 2.5)\n        plt.xticks(())\n        plt.yticks(())\n        plt.text(.99, .01, ('%.2fs' % (t1 - t0)).lstrip('0'),\n                 transform=plt.gca().transAxes, size=15,\n                 horizontalalignment='right')\n        plot_num += 1\n\nplt.show()"
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